> Does this mean that for any given prime, there will always be a prime within 600 digits? No. Euclid showed that the gap between consecutive primes can be arb

> Does this mean that for any given prime, there will always be a prime within 600 digits? No. Euclid showed that the gap between consecutive primes can be arbitrarily large. In particular, n!+2, n!+3, ..., n!+n are all composite whenever n>1. > Or that given a set of infinite numbers, you can also construct an infinite set of pairs of primes 600 digits apart? It means that there are infinitely many pairs of primes p and q such that 0 < |p - q| < 600.